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Følner Independence and the amenable Ising model

Published online by Cambridge University Press:  19 September 2008

Scot Adams
Scot Adams
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA
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Abstract

We define a criterion called Følner Independence for a stationary process over an amenable group. Intuitively, a process satisfies the criterion if, for sufficiently invariant Følner sets, the process in the Følner set is nearly independent of the process outside. We show that Følner Independence implies Finitely Determined. As an application, we show that, in its extreme Gibbs states, the amenable attractive Ising model is Følner Independent (hence Finitely Determined, hence Bernoulli).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 633 - 657
Copyright
Copyright © Cambridge University Press 1992

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References

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